The past two decades have witnessed the stagnation of the clock speed of microprocessors followed by the recent faltering of Moore's law as nanofabrication technology approaches its unavoidable physical limit. Vigorous efforts from various research areas have been made to develop power-efficient and ultrafast computing machines in this post-Moore's law era. With its unique capacity to integrate complex electro-optic circuits on a single chip, integrated photonics has revolutionized the interconnects and has shown its striking potential in optical computing. Here, we propose an electronic-photonic computing architecture for a wavelength division multiplexing-based electronic-photonic arithmetic logic unit, which disentangles the exponential relationship between power and clock rate, leading to an enhancement in computation speed and power efficiency as compared to the state-of-the-art transistors-based circuits. We experimentally demonstrate its practicality by implementing a 4-bit arithmetic logic unit consisting of 8 high-speed microdisk modulators and operating at 20 GHz. This approach paves the way to future power-saving and high-speed electronic-photonic computing circuits.